1 2 static char help[] = "Chemo-taxis Problems from Mathematical Biology.\n"; 3 4 /* 5 Page 18, Chemo-taxis Problems from Mathematical Biology 6 7 rho_t = 8 c_t = 9 10 Further discusson on Page 134 and in 2d on Page 409 11 */ 12 13 /* 14 15 Include "petscdmda.h" so that we can use distributed arrays (DMDAs). 16 Include "petscts.h" so that we can use SNES solvers. Note that this 17 file automatically includes: 18 petscsys.h - base PETSc routines petscvec.h - vectors 19 petscmat.h - matrices 20 petscis.h - index sets petscksp.h - Krylov subspace methods 21 petscviewer.h - viewers petscpc.h - preconditioners 22 petscksp.h - linear solvers 23 */ 24 25 #include <petscdm.h> 26 #include <petscdmda.h> 27 #include <petscts.h> 28 29 typedef struct { 30 PetscScalar rho, c; 31 } Field; 32 33 typedef struct { 34 PetscScalar epsilon, delta, alpha, beta, gamma, kappa, lambda, mu, cstar; 35 PetscBool upwind; 36 } AppCtx; 37 38 /* 39 User-defined routines 40 */ 41 extern PetscErrorCode IFunction(TS, PetscReal, Vec, Vec, Vec, void *), InitialConditions(DM, Vec); 42 43 int main(int argc, char **argv) 44 { 45 TS ts; /* nonlinear solver */ 46 Vec U; /* solution, residual vectors */ 47 DM da; 48 AppCtx appctx; 49 50 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 51 Initialize program 52 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 53 PetscFunctionBeginUser; 54 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 55 56 appctx.epsilon = 1.0e-3; 57 appctx.delta = 1.0; 58 appctx.alpha = 10.0; 59 appctx.beta = 4.0; 60 appctx.gamma = 1.0; 61 appctx.kappa = .75; 62 appctx.lambda = 1.0; 63 appctx.mu = 100.; 64 appctx.cstar = .2; 65 appctx.upwind = PETSC_TRUE; 66 67 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-delta", &appctx.delta, NULL)); 68 PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL)); 69 70 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 71 Create distributed array (DMDA) to manage parallel grid and vectors 72 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 73 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, 8, 2, 1, NULL, &da)); 74 PetscCall(DMSetFromOptions(da)); 75 PetscCall(DMSetUp(da)); 76 PetscCall(DMDASetFieldName(da, 0, "rho")); 77 PetscCall(DMDASetFieldName(da, 1, "c")); 78 79 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 80 Extract global vectors from DMDA; then duplicate for remaining 81 vectors that are the same types 82 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 83 PetscCall(DMCreateGlobalVector(da, &U)); 84 85 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 86 Create timestepping solver context 87 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 88 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 89 PetscCall(TSSetType(ts, TSROSW)); 90 PetscCall(TSSetDM(ts, da)); 91 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 92 PetscCall(TSSetIFunction(ts, NULL, IFunction, &appctx)); 93 94 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 95 Set initial conditions 96 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 97 PetscCall(InitialConditions(da, U)); 98 PetscCall(TSSetSolution(ts, U)); 99 100 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 101 Set solver options 102 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 103 PetscCall(TSSetTimeStep(ts, .0001)); 104 PetscCall(TSSetMaxTime(ts, 1.0)); 105 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 106 PetscCall(TSSetFromOptions(ts)); 107 108 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 109 Solve nonlinear system 110 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 111 PetscCall(TSSolve(ts, U)); 112 113 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 114 Free work space. All PETSc objects should be destroyed when they 115 are no longer needed. 116 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 117 PetscCall(VecDestroy(&U)); 118 PetscCall(TSDestroy(&ts)); 119 PetscCall(DMDestroy(&da)); 120 121 PetscCall(PetscFinalize()); 122 return 0; 123 } 124 /* ------------------------------------------------------------------- */ 125 /* 126 IFunction - Evaluates nonlinear function, F(U). 127 128 Input Parameters: 129 . ts - the TS context 130 . U - input vector 131 . ptr - optional user-defined context, as set by SNESSetFunction() 132 133 Output Parameter: 134 . F - function vector 135 */ 136 PetscErrorCode IFunction(TS ts, PetscReal ftime, Vec U, Vec Udot, Vec F, void *ptr) 137 { 138 AppCtx *appctx = (AppCtx *)ptr; 139 DM da; 140 PetscInt i, Mx, xs, xm; 141 PetscReal hx, sx; 142 PetscScalar rho, c, rhoxx, cxx, cx, rhox, kcxrhox; 143 Field *u, *f, *udot; 144 Vec localU; 145 146 PetscFunctionBegin; 147 PetscCall(TSGetDM(ts, &da)); 148 PetscCall(DMGetLocalVector(da, &localU)); 149 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE)); 150 151 hx = 1.0 / (PetscReal)(Mx - 1); 152 sx = 1.0 / (hx * hx); 153 154 /* 155 Scatter ghost points to local vector,using the 2-step process 156 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 157 By placing code between these two statements, computations can be 158 done while messages are in transition. 159 */ 160 PetscCall(DMGlobalToLocalBegin(da, U, INSERT_VALUES, localU)); 161 PetscCall(DMGlobalToLocalEnd(da, U, INSERT_VALUES, localU)); 162 163 /* 164 Get pointers to vector data 165 */ 166 PetscCall(DMDAVecGetArrayRead(da, localU, &u)); 167 PetscCall(DMDAVecGetArrayRead(da, Udot, &udot)); 168 PetscCall(DMDAVecGetArrayWrite(da, F, &f)); 169 170 /* 171 Get local grid boundaries 172 */ 173 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 174 175 if (!xs) { 176 f[0].rho = udot[0].rho; /* u[0].rho - 0.0; */ 177 f[0].c = udot[0].c; /* u[0].c - 1.0; */ 178 xs++; 179 xm--; 180 } 181 if (xs + xm == Mx) { 182 f[Mx - 1].rho = udot[Mx - 1].rho; /* u[Mx-1].rho - 1.0; */ 183 f[Mx - 1].c = udot[Mx - 1].c; /* u[Mx-1].c - 0.0; */ 184 xm--; 185 } 186 187 /* 188 Compute function over the locally owned part of the grid 189 */ 190 for (i = xs; i < xs + xm; i++) { 191 rho = u[i].rho; 192 rhoxx = (-2.0 * rho + u[i - 1].rho + u[i + 1].rho) * sx; 193 c = u[i].c; 194 cxx = (-2.0 * c + u[i - 1].c + u[i + 1].c) * sx; 195 196 if (!appctx->upwind) { 197 rhox = .5 * (u[i + 1].rho - u[i - 1].rho) / hx; 198 cx = .5 * (u[i + 1].c - u[i - 1].c) / hx; 199 kcxrhox = appctx->kappa * (cxx * rho + cx * rhox); 200 } else { 201 kcxrhox = appctx->kappa * ((u[i + 1].c - u[i].c) * u[i + 1].rho - (u[i].c - u[i - 1].c) * u[i].rho) * sx; 202 } 203 204 f[i].rho = udot[i].rho - appctx->epsilon * rhoxx + kcxrhox - appctx->mu * PetscAbsScalar(rho) * (1.0 - rho) * PetscMax(0, PetscRealPart(c - appctx->cstar)) + appctx->beta * rho; 205 f[i].c = udot[i].c - appctx->delta * cxx + appctx->lambda * c + appctx->alpha * rho * c / (appctx->gamma + c); 206 } 207 208 /* 209 Restore vectors 210 */ 211 PetscCall(DMDAVecRestoreArrayRead(da, localU, &u)); 212 PetscCall(DMDAVecRestoreArrayRead(da, Udot, &udot)); 213 PetscCall(DMDAVecRestoreArrayWrite(da, F, &f)); 214 PetscCall(DMRestoreLocalVector(da, &localU)); 215 PetscFunctionReturn(0); 216 } 217 218 /* ------------------------------------------------------------------- */ 219 PetscErrorCode InitialConditions(DM da, Vec U) 220 { 221 PetscInt i, xs, xm, Mx; 222 Field *u; 223 PetscReal hx, x; 224 225 PetscFunctionBegin; 226 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE)); 227 228 hx = 1.0 / (PetscReal)(Mx - 1); 229 230 /* 231 Get pointers to vector data 232 */ 233 PetscCall(DMDAVecGetArrayWrite(da, U, &u)); 234 235 /* 236 Get local grid boundaries 237 */ 238 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 239 240 /* 241 Compute function over the locally owned part of the grid 242 */ 243 for (i = xs; i < xs + xm; i++) { 244 x = i * hx; 245 if (i < Mx - 1) u[i].rho = 0.0; 246 else u[i].rho = 1.0; 247 u[i].c = PetscCosReal(.5 * PETSC_PI * x); 248 } 249 250 /* 251 Restore vectors 252 */ 253 PetscCall(DMDAVecRestoreArrayWrite(da, U, &u)); 254 PetscFunctionReturn(0); 255 } 256 257 /*TEST 258 259 test: 260 args: -pc_type lu -da_refine 2 -ts_view -ts_monitor -ts_max_time 1 261 requires: double 262 263 test: 264 suffix: 2 265 args: -pc_type lu -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time 1 266 requires: x double 267 output_file: output/ex4_1.out 268 269 TEST*/ 270